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Professor Matthias Winkel

Associate Professor of Probability

Bio

I studied in Münster and Manchester before doing my Ph.D. at the University of Paris 6 (now Sorbonne Université) under the supervision of Jean Bertoin. After a one-year pre- and post-doctoral stay in Aarhus working with Ole Barndorff-Nielsen, I joined the Department of Statistics at Oxford in April 2002.

Research Interests

  • Discrete and continuum random trees and forests, branching processes, superprocesses, tree-valued random processes

  • Exchangeability, random partitions, compositions, random hierarchies, interval partitions

  • Lévy processes, subordinators, time changes

Publications

Forman, N. et al. (2021) “Diffusions on a space of interval partitions: Poisson-Dirichlet stationary distributions”, Annals of Probability, 49(2), pp. 793–831.
Shi, Q. and Winkel, M. (2020) “Up-down ordered Chinese restaurant processes with two-sided immigration, emigration and diffusion limits.”
Forman, N. et al. (2020) “Diffusion on a space of interval partitions: Construction from marked Lévy processes”, Electronic Journal of Probability, 25.
Winkel, M. (2020) “Diffusions on a space of interval partitions: construction from Bertoin’s BES0(d), d ∈ (0, 1)”, Electronic Communications in Probability, 25, pp. 1–13.
Forman, N. et al. (2020) “Metrics on sets of interval partitions with diversity”, Electronic Communications in Probability, 25.
Forman, N. et al. (2020) “Projections of the Aldous chain on binary trees: Intertwining and consistency”, Random Structures and Algorithms, 57(3), pp. 745–769.
He, H. and Winkel, M. (2019) “Gromov–Hausdorff–Prokhorov convergence of vertex cut-trees of n-leaf Galton–Watson trees”, Bernoulli, 25(3), pp. 2301–2329.
Duquesne, T. and Winkel, M. (2018) “Hereditary tree growth and Lévy forests”, Stochastic Processes and their Applications, 129(10), pp. 3690–3747.
Pitman, J. and Winkel, M. (2018) “Squared Bessel processes of positive and negative dimension embedded in Brownian local times”, Electronic Communications in Probability, 23(2018).
Forman, N. et al. (2018) “Aldous diffusion I: a projective system of continuum $k$-tree evolutions.”

Contact Details

College affiliation: Supernumerary Fellow at Brasenose College

Email: winkel@stats.ox.ac.uk

Office: 3.12

Web: www.stats.ox.ac.uk/~winkel

Research Groups

Probability

Graduate Students

David Geldbach

Matthew Buckland

Gabriel Flath